Kinda, sorta. A recent Lancet study found that Omicron is two to four times less likely to cause long COVID than Delta:

Omicron long COVID and Delta long COVID indicate, for each stratum, the number of users with long COVID over the total number of users of that stratum.

That said, there are quite a few grains of salt here:

1. The roughly 0.25 odds ratios (a four-fold reduction in risk) seem to be driven more by the waning of the protective effect against Delta.
2. Related to the previous point, Delta shows an expected pattern: as time from vaccination increases, there is less protection against Delta. But Omicron is weird. Omicron shows the strongest effect, both in terms of odds ratios and raw percentages (i.e., independent of Delta) among those who were vaccinated over six months before the infection. This is puzzling.
3. We don’t know what symptoms are persisting. Some are more debilitating than others.
4. Like many glamour magz, there is a whole bunch of information that isn’t available to figure out these oddities–The Lancet is especially bad in this way. Makes for elegant stories, but it’s not that useful for actually learning stuff.
5. Even with the best case scenario with Omicron (and note point #2), we’re still seeing roughly two percent of respondents reporting long COVID.

That last point is critical: we are not seeing a negligible rate of long COVID among the vaccinated. Two percent isn’t nothing: if 100 million vaccinated people in the U.S. get infected, that’s still a lot of disabled people.

The Omicron numbers are actually better (less long COVID) than another UK study from May, so I think two percent is a reasonable estimate. Until we get better vaccines, or, at least, vaccines that are more effective at preventing long COVID, this isn’t over.